Joint estimation and compensation method of rf imperfections in lte uplink system

ABSTRACT

A joint estimation and compensation method of RF imperfections in a LIE (Long Term Evolution) uplink system comprises steps: establishing a joint signal model with RF imperfections; according to the joint signal model, undertaking estimation and compensation of CFO, DC offset, multipath channel, IQ imbalance and shaping filter imbalance of a received signal; and using a frequency equalizer to equalize said received signal and determine modulation data. For reducing computational complexity, the present invention further converts the received signal from a time domain to a frequency domain to undertake frequency domain compensation. The present invention can indeed solve the problems of IQ imbalance, filter imbalance, DC offset, multipath channel and CFO and effectively estimate and compensate RF imperfections in the LTE uplink system.

This application claims priority for Taiwan patent application no.104110066 filed on Mar. 27, 2015, the content of which is incorporatedby reference in its entirely.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an estimation and compensationtechnology for overcoming RF imperfections, particularly to a jointestimation and compensation method of RF imperfections, such as IQimbalance, shaping filter imbalance, DC offset, multipath channel andcarrier offset, in an uplink system.

2. Description of the Related Art

Succeeding to HSPA (High Speed Packet Access), LTE (Long Term Evolution)is a wireless access standard proposed by 3GPP (3rd GenerationPartnership Project) to achieve further higher transmission efficiency.ITU (International Telecommunication Union) has formally defined LTE as4G in 2010. LTE can enhance network transmission capacity and speed andsupport higher requirement of wireless communication.

According to the LTE specification proposed by 3GPP, an uplink systemuses SC-FDMA (Single Carrier Frequency Division Multiple Access)signals, and a downlink system uses OFDMA (Orthogonal Frequency DivisionMultiple Access) signals. The present invention is primarily involvedwith the technology of LTE uplink systems. Users of mobile devices oftencare about power consumption and price. Higher PAPR (Peak to AveragePower Ratio) will cause high price and high power consumption.Therefore, the LTE standard adopts the low power consumption SC-FDMAtechnology for uplink systems.

In an LTE uplink system, RF impairments are likely to occur in theDAC/RF device of the transmitter or receiver, such as IQ(In-phase/Quadrature-phase) imbalance, shaping filter imbalance, and DCoffset. In other words, the baseband transmitter generates complexbaseband signals; the baseband signals are divided into real parts (Isignals) and image parts (Q signals); the I signals and Q signals areprocessed by DAC and respectively multiplied by a cosine wave and a sinewave, which have an identical amplitude and an identical frequency buthave a phase difference of exactly 90 degrees; then, the signals arecarried by a radio frequency and transmitted. On receiving the signals,the receiver down-converts and demodulates the signals. However,mismatches are likely to occur between the oscillators respectivelygenerating sinusoidal waves in the transmitter and the receiver,including magnitude mismatches, phase mismatches, and oscillationfrequency mismatches. The magnitude mismatch is called the magnitudeimbalance. While the phases lack complete orthogonality, the phenomenonis called the phase imbalance. The two imbalances are called the IQimbalance in combination. On the other hand, the transmitter andreceiver must use a shaping filter to decrease the bandwidth of signalsso as to meet the demand of the system and reduce ISI (Inter-SymbolInterference). The Nyquist filter and the SRRC (Square Root RaiseCosine) filter are often used to shape the signals of the transmitterand the receiver. While the transmitter and the receiver respectivelyadopt different shaping filters, shaping filter imbalance may take placethere between. The cheaper direct-conversion architecture is often usedto reduce the cost. In such a case, a portion of the power of the localoscillator leaks to RF signals and mixes with the transmitted signals,which will cause IQ DC offset in the transmitter.

Besides, multipath propagation usually occurs in a wirelesscommunication system because of refraction, diffraction or scattering inan indoor or outdoor environment. In such a case, the receiver willreceive two or more signals from different paths in different delaytime, which will cause ISI and degrade the performance. Further, whileup- or down-conversion is undertaken between the transmitter and thereceiver, incomplete synchronization of the oscillators will causefrequency offset. Furthermore, Doppler shift occurring in high speedmovement will lead to CFO (Carrier Frequency Offset). CFO will seriouslyaffect the SC-FDMA- or OFDMA-based system, not only interfering withwireless communication but also leading to ICI (Inter-CarrierInterference).

The signal imbalances, such as IQ imbalance, shaping filter imbalance,DC offset, multipath channel, and CFO, will lead to RF mismatch in anLTE uplink system. At present, most of the related technologiesundertake estimation and compensation in the frequency domain. However,they do not apply to LTE uplink systems. So far, neither a jointestimation nor a joint compensation method has been published, not tomention a time-domain joint estimation and compensation methodconsidering various RF attenuations.

Accordingly, the present invention proposes a joint estimation andcompensation method of RF imperfection in an uplink system to overcomeall the imperfections in LTE uplink systems.

SUMMARY OF THE INVENTION

The primary objective of the present invention is to provide a jointestimation and compensation method of RF imperfections in an uplinksystem, which undertakes joint estimation and compensation of signalimbalances in a time domain to overcome IQ imbalance, shaping filterimbalance, DC offset, multipath channel, and carrier frequency offset ofLTE uplink systems, and which exempts the LTE uplink systems from theaffection of the IQ mismatch generated by a direct-conversiontransmitter or receiver, whereby to effectively estimate and compensatefor the RF mismatch of LTE uplink systems.

Another objective of the present invention is to provide a jointestimation and compensation method of RF imperfections in an uplinksystem, which takes different RF attenuations into considerationsimultaneously and undertakes estimation and compensation jointly in thetime domain.

A further objective of the present invention is to provide alow-complexity frequency-domain compensator.

To achieve the abovementioned objectives, the present invention proposesa joint estimation and compensation method, which comprises steps:establishing a joint signal model with RF imperfections; according tothe joint signal model, undertaking an initial CFO (Carrier FrequencyOffset) estimation of a received signal in a time domain so as toestimate the CFO parameter and compensate the received signal;estimating DC offset, multipath channel, imbalance signals in the jointsignal model of the received signal and compensating the received signalin the time domain; then determining the modulation data. In order toincrease the feasibility of testing the system, the present inventionfurther proposes a time-domain compensation method, which greatlyreduces the computation of matrix conversions and multiplications,whereby the cost of developing chips is decreased and the efficiency ofthe system is optimized.

After the estimation of the initial transmitted signal has beenacquired, whether the error vector magnitude converges is verified. Ifthe error vector magnitude does not converge, the decision-directedsymbol is used to undertake iterative CFO estimation and compensation soas to undertake further estimation and compensation of RF imperfectionsuntil the error vector magnitude converges. If the error vectormagnitude converges, the gain mismatch parameter and phase mismatchparameter of the joint signal model are estimated according to theimbalance parameters.

Below, embodiments are described in detail in cooperation with theattached drawings to make easily understood the objectives, technicalcontents, and accomplishments of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram schematically showing the architecture of an uplinksystem used by the present invention;

FIG. 2 shows a flowchart of a joint estimation and compensation methodof RF imperfections in an uplink system according to one embodiment ofthe present invention;

FIG. 3 is a diagram schematically showing an LTE signal analysis systemused by the present invention;

FIG. 4(a) shows EVM of the performance analysis results of an R&S LTEsignal analyzer;

FIG. 4(b) shows a constellation map of the performance analysis resultsof an R&S LTE signal analyzer;

FIG. 5(a) shows a constellation map of PUSCH signals, wherein RFimperfections have been compensated by the present invention;

FIG. 5(b) shows a constellation map of DMRS signals, wherein RFimperfections have been compensated by the present invention; and

FIG. 6 shows a captured image of EVM performance of PUSCH signals andDMRS signals of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention discloses a joint estimation and compensationmethod of RF imperfections in an uplink system to solve the problems ofIQ imbalance, filter imbalance, DC offset, multipath channel and CFO(Carrier Frequency Offset) in a LTE uplink system so as to effectivelyestimate and compensate for RF mismatch in the LTE uplink system.

Refer to FIG. 1 for the architecture of an uplink system used by thepresent invention. In a transmitter 1, the demodulated data passes a DFT(Discrete Fourier Transform) unit 11, a subcarrier mapping unit 12 andan IDFT (Inverse DFT) unit 13 in sequence, and has a ½ frequency offset(Δf) in the IDFT unit 13. Next, a CP (Cyclic Prefix) unit 14 adds cyclicprefixes to the signal. Next, a parallel-to-serial conversion unit 15converts the parallel signal into a serial signal. Then, a DAC/RFemitting unit 16 converts the signal into an analog signal and transmitsthe analog signal. The signal is transmitted to a receiver 2 via achannel 3. In the receiver 2, the received signal passes an RFreceiving/ADC unit 21, a packet detection unit 22 and an equalizer 23 insequence. The equalizer 23 estimates and compensates for RFimperfections and removes the ½ frequency offset (Δf). Next, aserial-to-parallel conversion unit 24 converts the serial signal into aparallel signal. Next, a CP removing unit 25 removes the cyclicprefixes. Next, the signal passes a DFT unit 26, a subcarrier demappingunit 27 and an IDFT (Inverse DFT) unit 28. Then, the demodulated data isoutput. Between the transmitter 1 and the receiver 2, there are problemsof IQ imbalances, DC offset, multipath channel, and carrier frequencyoffset, which will be estimated and compensated jointly in the equalizer23.

Refer to FIG. 2 for a flowchart of a joint estimation and compensationmethod of RF imperfections in an uplink system according to oneembodiment of the present invention. In Step S10, establish a jointsignal model with RF imperfections, including CFO (Carrier FrequencyOffset), DC offset, multipath channel, IQ imbalance and shaping filterimbalance. In Step S12, after the receiver 2 receives the signal, use atraining sequence in a time domain to undertake an estimation of theinitial CFO of the received signal according to the joint signal modelso as to estimate the CFO parameters and compensate the received signal.In Step S14, after CFO have been compensated, use the training sequenceto undertake an estimation and compensation of the initial phase of thereceived signal. In Step S16, use the training sequence in a time domainto undertake a joint estimation of the DC offset, multipath channel, andsignal imbalance of the joint signal model so as to compensate for allthe RF imperfection factors of the received signal, wherein the signalimbalance includes IQ imbalance and shaping filter imbalance. In StepS18, after the abovementioned estimation and compensation, determine themodulation data so as to resume the original transmitted signal. In StepS20, after the modulation data has been determined, determine whetherEVM (Error Vector Magnitude) converges. If yes, the process proceeds toStep S24. If EVM does not converge, the process proceeds to Step S22. InStep S22, use decision-directed symbols to undertake iterative CFOestimation and compensation, and then return to Step S14 to undertakethe abovementioned steps to make further estimation and compensation ofRF imperfection factors until EVM converges. If EVM converges in StepS20, the process proceeds to Step S24. In Step S24, use imbalanceparameters, including IQ imbalance parameters and filter imbalanceparameters, to estimate the parameters of gain mismatch and phasemismatch in the joint signal model. The magnitude imbalance and phaseimbalance of IQ imbalance can also be learned in Step S24. Thus arecompletely solved the problems of IQ imbalance, shaping filterimbalance, DC offset, multipath channel, and carrier frequency offset inLTE uplink systems. Further is eliminated the affection of IQ mismatchcaused by a direct-conversion transceiver. Therefore, the presentinvention can effectively estimate and compensate for RF imperfectionsof LTE uplink systems.

In order to demonstrate the signal processing steps in detail and makeeasily understood the technical characteristics of the presentinvention, the method of the present invention will be described inthree parts from simple to complex: 1. joint estimation and compensationof IQ imbalance and shaping filter imbalance; 2. joint estimation andcompensation of IQ imbalance, shaping filter imbalance, IQ DC offset andmultipath channel; 3. joint estimation and compensation of IQ imbalanceand shaping filter imbalance, IQ DC offset, multipath channel andcarrier frequency offset. The three parts will be described step by stepin sequence to make readers fully appreciate the technical contents ofthe present invention.

Firstly is described a time-domain joint estimation and compensationarchitecture of IQ imbalance and shaping filter imbalance, which caneliminate the affection of IQ mismatch caused by a direct-conversiontransceiver. Suppose perfect synchronization exists in a joint signalmodel with IQ imbalance and shaping filter imbalance. Aftersynchronization and down-sampling, the received signal y can beexpressed by Equation 1.1:

y=h ₁

ũ+h ₂

ũ*  1.1

wherein the length of y is L, and wherein the coefficients h₁ and h₂ isinvolved with RF imperfections, including IQ imbalance and shapingfilter imbalance, and can be expressed by Equation 1.2:

$\begin{matrix}\left\{ \begin{matrix}{h_{1} = {\frac{1}{2}\left( {h_{C,I} + {h_{C,Q}g_{T}^{j\; \varphi_{T}}}} \right)}} \\{h_{2} = {\frac{1}{2}\left( {h_{C,I} - {h_{C,Q}g_{T}^{j\; \varphi_{T}}}} \right)}}\end{matrix} \right. & 1.2\end{matrix}$

Wherein h_(C,I) and h_(C,Q) are respectively the real-part shapingfilter imbalance parameter and the imaginary-part shaping filterimbalance parameter, and can be expressed by Equation 1.3:

$\begin{matrix}\left\{ \begin{matrix}{h_{C,I} = {{{Re}{\left\{ h_{RX} \right\} \otimes {Re}}\left\{ h_{TX} \right\}} = {h_{{RX},I} \otimes h_{{TX},I}}}} \\{h_{C,Q} = {{{Im}{\left\{ h_{RX} \right\} \otimes {Im}}\left\{ h_{TX} \right\}} = {h_{{RX},Q} \otimes h_{{TX},Q}}}}\end{matrix} \right. & 1.3\end{matrix}$

Wherein Re{·} and Im{·} respectively denote the real part and theimaginary part.

A training sequence can be used to estimate the joint signal with IQimbalance and shaping filter imbalance. A DMRS (demodulation referencesignal) sequence is used as the training sequence and substituted intoEquation 1.1. Thus is obtained Equation 1.4:

$\begin{matrix}\begin{matrix}{y = {{h_{1} \otimes \overset{\sim}{c}} + {h_{2} \otimes {\overset{\sim}{c}}^{*}}}} \\{= {{\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}}}} \\{= {\overset{\sim}{\overset{\sim}{C}}\begin{bmatrix}{\overset{\sim}{h}}_{1} \\{\overset{\sim}{h}}_{2}\end{bmatrix}}}\end{matrix} & 1.4\end{matrix}$

wherein the parameters are respectively defined by Equations 1.5-1.9:

{tilde over (h)} ₁=diag{e ₀ ,e ⁻¹ , . . . ,e _(−L+1) }h ₁  1.5

{tilde over (h)} ₂=diag{e ₀ *,e ⁻¹ *, . . . ,e _(−L+1) *}h ₂  1.6

e _(−n) =e ^(jπ(−n)/N) ,n=0,1, . . . ,L−1  1.7

h ₁ =[h _(1,−L/2) ,h _(1,−L/2+1) , . . . ,h _(1,L/2−1) ,h_(1,L/2)]^(T)  1.8

h ₂ =[h _(2,−L/2) ,h _(2,−L/2+1) , . . . ,h _(2,L/2−1) ,h_(2,L/2)]^(T)  1.9

wherein {tilde over ({tilde over (C)})}=[{tilde over (C)}{tilde over(C)}*] is a N by (L+1) matrix C which involves a circular convolutionmatrix of a training sequence {tilde over (c)} with Δf=½ offset. {tildeover (c)}=[{tilde over (c)}(0){tilde over (c)}(1) . . . {tilde over(c)}(N−1)] is a Chu sequence with a length of N and Δf=½, which isexpressed by Equation 1.10.

$\begin{matrix}{\overset{\sim}{C} = {E\begin{bmatrix}{c(0)} & {c\left( {N - 1} \right)} & \cdots & {c(1)} \\{c(1)} & {c(0)} & \cdots & {c(2)} \\\vdots & \vdots & \ddots & \vdots \\{c\left( {N - 1} \right)} & {c\left( {N - 2} \right)} & \cdots & {c(0)}\end{bmatrix}}_{N \times L}} & 1.10\end{matrix}$

wherein E=diag {e₀, e₁, . . . , e_(N−1)} is a diagonal matrixrepresenting Δf=½ offset.

According to Equation 1.4, the parameters of IQ imbalance and shapingfilter imbalance can be estimated with a pseudo inverse matrix expressedby Equation 1.11:

$\begin{matrix}{\begin{bmatrix}{\hat{\overset{\sim}{h}}}_{1} \\{\hat{\overset{\sim}{h}}}_{2}\end{bmatrix} = {{{\overset{\sim}{\overset{\sim}{C}}}^{\dagger}y} = {\left( {{\overset{\sim}{\overset{\sim}{C}}}^{H}\overset{\sim}{\overset{\sim}{C}}} \right)^{- 1}{\overset{\sim}{\overset{\sim}{C}}}^{H}y}}} & 1.11\end{matrix}$

Assumed that {tilde over (ĥ)}₁ and {tilde over (ĥ)}₂, and jointparameters of IQ imbalance and shaping filter imbalance can be estimatedperfectly. The time-domain compensation of the received signal asexpressed by Equation 1.1 is expressed by Equation 1.12:

$\begin{matrix}\begin{matrix}{y = {{h_{1} \otimes \overset{\sim}{u}} + {h_{2} \otimes {\overset{\sim}{u}}^{*}}}} \\{= {{E{\overset{\sim}{H}}_{1}u} + {E^{*}{\overset{\sim}{H}}_{2}u^{*}}}} \\{= {{{\overset{\sim}{\overset{\sim}{H}}}_{1}u} + {{\overset{\sim}{\overset{\sim}{H}}}_{2}u^{*}}}} \\{= {{\left( {{\overset{\sim}{\overset{\sim}{H}}}_{1,I} + {j{\overset{\sim}{\overset{\sim}{H}}}_{1,Q}}} \right)\left( {u_{I} + {ju}_{Q}} \right)} + {\left( {{\overset{\sim}{\overset{\sim}{H}}}_{2,I} + {j{\overset{\sim}{\overset{\sim}{H}}}_{2,Q}}} \right)\left( {u_{I} - {ju}_{Q}} \right)}}}\end{matrix} & 1.12\end{matrix}$

wherein both {tilde over ({tilde over (H)})}₁ and {tilde over ({tildeover (H)})}₂ involve imbalance coefficients, which has Δf=½ offset, ofjoint estimation of Q imbalance and shaping filter imbalance areexpressed by Equations 1.13-1.16.

$\begin{matrix}\begin{matrix}{{\overset{\sim}{\overset{\sim}{H}}}_{1} = {E{\overset{\sim}{H}}_{1}}} \\{= {E\begin{bmatrix}{\overset{\sim}{h}}_{1,{{- L}\text{/}2}} & 0 & \cdots & {\overset{\sim}{h}}_{1,{{{- L}\text{/}2} + 1}} \\{\overset{\sim}{h}}_{1,{{{- L}\text{/}2} + 1}} & {\overset{\sim}{h}}_{1,{{- L}\text{/}2}} & \cdots & \vdots \\\vdots & {\overset{\sim}{h}}_{1,{{{- L}\text{/}2} + 1}} & \cdots & {\overset{\sim}{h}}_{1,{L\text{/}2}} \\{\overset{\sim}{h}}_{1,{L\text{/}2}} & \vdots & \cdots & 0 \\0 & {\overset{\sim}{h}}_{1,{L\text{/}2}} & \cdots & \vdots \\\vdots & 0 & \ddots & 0 \\0 & 0 & \cdots & {\overset{\sim}{h}}_{1,{{- L}\text{/}2}}\end{bmatrix}}}\end{matrix} & 1.13 \\{\begin{matrix}{{\overset{\sim}{\overset{\sim}{H}}}_{2} = {E{\overset{\sim}{H}}_{2}}} \\{= {E\begin{bmatrix}{\overset{\sim}{h}}_{2,{{- L}\text{/}2}} & 0 & \cdots & {\overset{\sim}{h}}_{2,{{{- L}\text{/}2} + 1}} \\{\overset{\sim}{h}}_{2,{{{- L}\text{/}2} + 1}} & {\overset{\sim}{h}}_{2,{{- L}\text{/}2}} & \cdots & \vdots \\\vdots & {\overset{\sim}{h}}_{2,{{{- L}\text{/}2} + 1}} & \cdots & {\overset{\sim}{h}}_{2,{L\text{/}2}} \\{\overset{\sim}{h}}_{2,{L\text{/}2}} & \vdots & \cdots & 0 \\0 & {\overset{\sim}{h}}_{2,{L\text{/}2}} & \cdots & \vdots \\\vdots & 0 & \ddots & 0 \\0 & 0 & \cdots & {\overset{\sim}{h}}_{2,{{- L}\text{/}2}}\end{bmatrix}}}\end{matrix}{wherein}} & 1.14 \\{{\overset{\sim}{h}}_{1} = \begin{bmatrix}{h_{1,{{- L}\text{/}2}} \cdot e_{0}} \\{h_{1,{{{- L}\text{/}2} + 1}} \cdot e_{- 1}} \\\vdots \\{h_{1,{L\text{/}2}} \cdot e_{{- L} + 1}}\end{bmatrix}} & 1.15 \\{{\overset{\sim}{h}}_{2} = \begin{bmatrix}{h_{2,{{- L}\text{/}2}} \cdot e_{0}^{*}} \\{h_{2,{{{- L}\text{/}2} + 1}} \cdot e_{- 1}^{*}} \\\vdots \\{h_{2,{L\text{/}2}} \cdot e_{{- L} + 1}^{*}}\end{bmatrix}} & 1.16\end{matrix}$

The real part and the imaginary part can be cascaded in Equation 1.12.Thus, the received signal matrix can be acquired with Equation 1.17:

$\begin{matrix}{\begin{bmatrix}y_{I} \\y_{Q}\end{bmatrix} = {\underset{\begin{matrix} \\H\end{matrix}}{\begin{bmatrix}{{\overset{\sim}{\overset{\sim}{H}}}_{1,I} + {\overset{\sim}{\overset{\sim}{H}}}_{2,I}} & {{\overset{\sim}{\overset{\sim}{H}}}_{2,Q} - {\overset{\sim}{\overset{\sim}{H}}}_{1,Q}} \\{{\overset{\sim}{\overset{\sim}{H}}}_{1,Q} + {\overset{\sim}{\overset{\sim}{H}}}_{2,Q}} & {{\overset{\sim}{\overset{\sim}{H}}}_{1,I} - {\overset{\sim}{\overset{\sim}{H}}}_{2,I}}\end{bmatrix}}\begin{bmatrix}u_{I} \\u_{Q}\end{bmatrix}}} & 1.17\end{matrix}$

It is learned from Equation 1.17: H is an estimated signal imbalancematrix including IQ imbalance and shaping filter imbalance.y=y_(I)+jy_(Q) represents the received signal with RF effect.u=u_(I)+ju_(Q) is the SC-FDMA transmitted signal for the uplink system.The received signal whose IQ imbalance and shaping filter imbalance hasbeen compensated can be expressed by Equation 1.18:

$\begin{matrix}{\begin{bmatrix}{\hat{u}}_{I} \\{\hat{u}}_{Q}\end{bmatrix} = {{\hat{H}}^{- 1}\begin{bmatrix}y_{I} \\y_{Q}\end{bmatrix}}} & 1.18\end{matrix}$

In order to reduce the computational complexity of the receiver, a lowcomplexity frequency domain receiver is designed by the following steps.According to Equation 1.12, the time-domain received signal can beexpressed by Equation 1.19:

$\begin{matrix}\begin{matrix}{y = {{h_{1} \otimes \overset{\sim}{u}} + {h_{2} \otimes {\overset{\sim}{u}}^{*}}}} \\{= {{E{\overset{\sim}{H}}_{1}u} + {E^{*}{\overset{\sim}{H}}_{2}u^{*}}}}\end{matrix} & 1.19\end{matrix}$

Firstly, a known matrix E* can be used to compensate for Δf=½ offset asshown in Equation 1.20:

$\begin{matrix}\begin{matrix}{\overset{\sim}{y} = {E^{*}y}} \\{= {{{\overset{\sim}{H}}_{1}u} + {\left( E^{*} \right)^{2}{\overset{\sim}{H}}_{2}u^{*}}}}\end{matrix} & 1.20\end{matrix}$

wherein u=[u(0)u(N−1) . . . u(1)]^(T) is the received signal vector inthe time domain, which needs equalization.

Next, the received signal can be expressed by Equation 1.21 in afrequency domain:

$\begin{matrix}\begin{matrix}{{\overset{\sim}{y}}_{f} = {F\overset{\sim}{y}}} \\{= {{{FF}^{H}{\overset{\sim}{\Lambda}}_{1}{Fu}} + {{F\left( E^{*} \right)}^{2}F^{H}{\overset{\sim}{\Lambda}}_{2}{ABFu}^{*}}}} \\{= {{{\overset{\sim}{\Lambda}}_{1}u_{f}} + {{\overset{\_}{\Lambda}}_{2}{\overset{\_}{u}}_{f}^{*}}}}\end{matrix} & 1.21\end{matrix}$

Wherein F is an FFT matrix, and the other parameters in Equation 1.21are respectively defined by Equations 1.22-1.28:

$\begin{matrix}{{\overset{\sim}{H}}_{1} = {F^{H}{\overset{\sim}{\Lambda}}_{1}F}} & 1.22 \\\begin{matrix}{{\overset{\sim}{H}}_{2} = {F^{H}{\overset{\sim}{\Lambda}}_{2}F}} \\{= {F^{H}{\overset{\sim}{\Lambda}}_{2}{ABF}}}\end{matrix} & 1.23 \\{{\overset{\_}{\Lambda}}_{2} = {{F\left( E^{*} \right)}^{2}F^{H}{\overset{\sim}{\Lambda}}_{2}A}} & 1.24 \\\begin{matrix}{{\overset{\_}{u}}_{f}^{*} = {BFu}^{*}} \\{= {Bu}_{f}} \\{= \left\lbrack {{u_{f}^{*}\left( {N - 1} \right)}\mspace{14mu} {u_{f}^{*}\left( {N - 2} \right)}\mspace{14mu} \cdots \mspace{14mu} {u_{f}^{*}(0)}} \right\rbrack^{T}}\end{matrix} & 1.25 \\{A = \begin{bmatrix}0 & 0 & 0 & \cdots & 1 \\1 & 0 & 0 & \cdots & 0 \\0 & 1 & 0 & \cdots & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots \\0 & 0 & 0 & \cdots & 0\end{bmatrix}} & 1.26 \\{B = \begin{bmatrix}0 & 1 & 0 & \cdots & 0 \\0 & 0 & 1 & \cdots & 0 \\0 & 0 & 0 & \cdots & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots \\1 & 0 & 0 & \cdots & 0\end{bmatrix}} & 1.27 \\{{AB} = I} & 1.28\end{matrix}$

wherein I is an identity matrix.

Via using {tilde over (Ĥ)}₁, {tilde over (Ĥ)}₂, {tilde over ({circumflexover (Λ)})}₁, and {tilde over ({circumflex over (Λ)})}₂, which areacquired in estimating {tilde over (ĥ)}₁ and {tilde over (ĥ)}₂, the mthand (N−1−m)th elements of {tilde over (y)}_(f)(n) can be expressed byEquation 1.29:

$\begin{matrix}{{\begin{bmatrix}{{\overset{\sim}{y}}_{f}\left( {n,m} \right)} \\{{\overset{\sim}{y}}_{f}^{*}\left( {n,{N - 1 - m}} \right)}\end{bmatrix} = {\underset{\begin{matrix} \\{\overset{\sim}{\Lambda}{(m)}}\end{matrix}}{\begin{bmatrix}{{\overset{\sim}{\Lambda}}_{1}\left( {m,m} \right)} & {{\overset{\_}{\Lambda}}_{2}\left( {m,m} \right)} \\{{\overset{\_}{\Lambda}}_{2}^{*}\left( {m,{N - 1 - m}} \right)} & {{\overset{\sim}{\Lambda}}_{1}^{*}\left( {m,{N - 1 - m}} \right)}\end{bmatrix}}\begin{bmatrix}{u_{f}\left( {n,m} \right)} \\{u_{f}^{*}\left( {n,{N - 1 - m}} \right)}\end{bmatrix}}},{0 \leq m \leq {\frac{N}{2} - 1}}} & 1.29\end{matrix}$

The joint RF effect coefficient {tilde over (Λ)} can be removed viamultiplying the frequency-domain received signal with the inverse matrixcoefficient {tilde over (Λ)}⁻¹ according to Equation 1.30:

$\begin{matrix}{\begin{bmatrix}{{\hat{u}}_{f}\left( {n,m} \right)} \\{{\hat{u}}_{f}^{*}\left( {n,{N - 1 - m}} \right)}\end{bmatrix} = {{{\overset{\sim}{\Lambda}}^{- 1}(m)}\begin{bmatrix}{{\overset{\sim}{y}}_{f}\left( {n,m} \right)} \\{{\overset{\sim}{y}}_{f}^{*}\left( {n,{N - 1 - m}} \right)}\end{bmatrix}}} & 1.30\end{matrix}$

After equalization, the original frequency-domain transmitted signalû_(f)=[û_(f)(n,0)û_(f)(n,1) . . . û_(f)(n,N−1)]^(T) can be acquired.Then, an IFFT (F^(H)) operator is used to acquire the originaltime-domain signal according to Equation 1.31, and the desiredtransmitted signal is transformed from the frequency domain to the timedomain.

$\begin{matrix}\begin{matrix}{\hat{u} = {F^{H}{\hat{u}}_{f}}} \\{= \left\lbrack {{\hat{u}\left( {n,0} \right)}\mspace{14mu} {\hat{u}\left( {n,1} \right)}\mspace{14mu} \cdots \mspace{14mu} {\hat{u}\left( {n,{N - 1}} \right)}} \right\rbrack^{T}}\end{matrix} & 1.31\end{matrix}$

On the other hand, the IQ-imbalance joint signal model is influenced bygain mismatch and phase mismatch, which will cause serious degradationin the system. Therefore, it is necessary to accurately calculate thegain mismatch parameter g_(T) and the phase mismatch parameter φ_(T) inaddition to estimating and compensating RF problems.

After {tilde over (h)}₁ and {tilde over (h)}₁ has been estimated, theeffects of IQ imbalance and shaping filter imbalance are equalized,wherein the Nyquist filter is used in the transmitter and the SRRCfilter is used in the receiver. Suppose the I-channel filter andQ-channel composite filter are similar (h_(C,I)=h_(C,Q)) In other words,identical mismatches occur in I-channel filter imbalance and Q-channelfilter imbalance. For example, h_(C,I)=h_(RX,I)

h_(TX,I) and h_(C,Q)=h_(RX,Q)

h_(TX,Q). From the above discuss, it is learned: the joint IQ imbalanceand shaping filter imbalance can be modeled into

$h_{1} = {{\frac{1}{2}\left( {h_{C,I} + {h_{C,Q}g_{T}^{j\; \varphi_{T}}}} \right)\mspace{14mu} {and}\mspace{14mu} h_{2}} = {\frac{1}{2}{\left( {h_{C,I} - {h_{C,Q}g_{T}^{j\; \varphi_{T}}}} \right).}}}$

Therefore, h₁ and h₂ can be used to estimate g_(T) and φ_(T) withaddition and subtraction technologies according to Equation 1.32 andEquation 1.33:

$\begin{matrix}{h_{s} = {{h_{1} + h_{2}} = h_{C,I}}} & 1.32 \\\begin{matrix}{h_{d} = {h_{1} - h_{2}}} \\{{= {h_{C,Q}g_{T}^{j\; \varphi_{T}}}}} \\{{\approx {h_{C,I}g_{T}^{j\; \varphi_{T}}}}}\end{matrix} & 1.33\end{matrix}$

According to Equation 1.32 and Equation 1.33, a correlation method usesh_(s) and h_(d) to obtain g_(T) and φ_(T) with Equation 1.34 andEquation 1.35:

$\begin{matrix}\begin{matrix}{h_{r} = {h_{s}^{H}h_{d}}} \\{= \left. ||h_{C,I}||{}_{2}{g_{T}^{j\; \varphi_{T}}} \right.}\end{matrix} & 1.34 \\\begin{matrix}{{\overset{\_}{h}}_{r} = \frac{h_{r}}{\left. ||h_{s} \right.||^{2}}} \\{= {g_{T}^{{j\varphi}_{T}}}}\end{matrix} & 1.35\end{matrix}$

The obtained g_(T) and φ_(T) are shown in Equation 1.36:

$\begin{matrix}\left\{ \begin{matrix}{{\hat{g}}_{T} = \left| {\overset{\_}{h}}_{r} \right|} \\{{\hat{\varphi}}_{T} = {\tan^{- 1}\left( {\overset{\_}{h}}_{r} \right)}}\end{matrix} \right. & 1.36\end{matrix}$

Part I of the description of the method of the present invention, whichinvolves the joint signal model with IQ imbalance and shaping filterimbalance, has been stated above. Part II, which involves a joint signalfurther with DC offset and multipath channel, will be described below.

In Part II, a joint estimation and compensation architecture of IQimbalance, shaping filter imbalance, DC offset and multipath channel toeliminate the IQ mismatch caused by a direct-conversion transceiver willbe described. The received signal of a joint signal model with IQimbalance, shaping filter imbalance, DC offset and multipath channel canbe expressed by Equation 2.1:

y=h ₁

(ũ+d1)+h ₂

(ũ*+d*1)  2.1

wherein h₁ and h₂ are joint models also involving IQ imbalance parameterand shaping filter imbalance parameter similar to those in Equation 1.2,and wherein d denotes IQ DC offset and Vector I is an N×1 vector of allones.

However, h₁ and h₂ involve filter imbalance coefficients h_(C,I) andh_(C,Q), which are convoluted with multipath channel h_(ch). Theestimation and compensation method in Part II will be integrated withthat of Part I and is expressed by Equation 2.2.

$\begin{matrix}\left\{ \begin{matrix}{h_{C,I} = {{Re}{\left\{ h_{RX} \right\} \otimes {Re}}\left\{ {h_{ch} \otimes h_{TX}} \right\}}} \\{h_{C,Q} = {{Im}{\left\{ h_{RX} \right\} \otimes {Im}}\left\{ {h_{ch} \otimes h_{TX}} \right\}}}\end{matrix} \right. & 2.2\end{matrix}$

wherein h_(ch) denotes multipath channel.

These problems can be estimated with a DMRS training sequence. Thereceived signal can be represented by a convolution matrix expressed byEquation 2.3:

y=h ₁

{tilde over (c)}+h ₂

{tilde over (c)}*+h ₁

d1+h ₂

d*1={tilde over (C)}{tilde over (h)} ₁ +{tilde over (C)}*{tilde over(h)} ₂ +dDh ₁ +d*Dh ₂  2.3

wherein D is a circular convolution matrix of all 1 vectors, and wherein{tilde over (C)} is a N by L+1 circular convolution matrix of thetraining sequence with Δf=½ offset, as shown in Equation 2.4-2.6.

$\begin{matrix}{\overset{\sim}{C} = {E\begin{bmatrix}{c(0)} & {c\left( {N - 1} \right)} & \cdots & {c(1)} \\{c(1)} & {c(0)} & \cdots & {c(2)} \\\vdots & \vdots & \ddots & \vdots \\{c\left( {N - 1} \right)} & {c\left( {N - 2} \right)} & \cdots & {c(0)}\end{bmatrix}}_{N \times {({L + 1})}}} & 2.4 \\{{\overset{\sim}{h}}_{1} = {{diag}\left\{ {e_{0},e_{- 1},\cdots,e_{- L}} \right\} h_{1}}} & 2.5 \\{{\overset{\sim}{h}}_{2} = {{diag}\left\{ {e_{0}^{*},e_{- 1}^{*},\cdots,e_{- L}^{*}} \right\} h_{2}}} & 2.6\end{matrix}$

In order to remove the DC offset in the frequency domain, the receivedsignal is processed with post-FFT and expressed by Equation 2.7:

$\begin{matrix}\begin{matrix}{y_{f} = {Fy}} \\{= {{F\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {F{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}} + {{dFDF}^{H}{Fh}_{1}} + {d^{*}{FDF}^{H}{Fh}_{2}}}}\end{matrix} & 2.7\end{matrix}$

wherein F^(H)F is an identity matrix, and wherein

$\begin{matrix}\begin{matrix}{{FDF}^{H} = \Lambda_{DC}} \\{= {{diag}\left\{ {\lambda_{DC},0,\ldots,0} \right\}}}\end{matrix} & 2.8\end{matrix}$

wherein Λ_(DC) is a diagonal matrix with only the eigenvalue λ₁₁, andthe other elements are zero. Thereby, the IQ DC offset can be removedeasily.

Therefore, from Equation 2.7, the post-FFT received data can bemultiplied by a T matrix (an (N−1)×N matrix) to eliminate the componentof IQ DC offset according to Equation 2.9:

$\begin{matrix}{\begin{matrix}{{\overset{\_}{y}}_{f} = {TFy}} \\{= {{F_{T}\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {F_{T}{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}} + {{dF}_{T}{DF}^{H}{Fh}_{1}} + {d^{*}F_{T}{DF}^{H}{Fh}_{2}}}}\end{matrix}{wherein}} & 2.9 \\{F_{T} = {TF}} & 2.10 \\{{F_{T}{DF}^{H}} = {{T\; \Lambda_{DC}} = O_{{({N - 1})} \times N}}} & 2.11 \\{T = \left\lbrack o_{{({N - 1})} \times 1} \middle| I_{{({N - 1})} \times {({N - 1})}} \right\rbrack} & 2.12\end{matrix}$

wherein O is an (N−1)×N matrix of all zeros, o is an (N−1)×1 vector ofall zeros, and I is an identity matrix. Therefore, Matrix T can be usedto eliminate the component of IQ DC offset.

After IQ DC offset is removed, y _(f) is obtained according to Equation2.13:

$\begin{matrix}\begin{matrix}{{\overset{\_}{y}}_{f} = {{F_{T}\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {F_{T}{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}}}} \\{= {\overset{\sim}{\overset{\sim}{C}}\begin{bmatrix}{\overset{\sim}{h}}_{1} \\{\overset{\sim}{h}}_{2}\end{bmatrix}}}\end{matrix} & 2.13\end{matrix}$

wherein {tilde over ({tilde over (C)})}=[F_(T){tilde over(C)}F_(T){tilde over (C)}*] is a composite training sequence matrix inthe frequency domain.

Similarly to the approach to obtain Equation 1.11, a LS (Least Square)algorithm can be used to estimate {tilde over (ĥ)}₁ and {tilde over(ĥ)}₂ according to Equation 2.14.

$\begin{matrix}{\begin{bmatrix}{\hat{\overset{\sim}{h}}}_{1} \\{\hat{\overset{\sim}{h}}}_{2}\end{bmatrix} = {{{\overset{\sim}{\overset{\sim}{C}}}^{\dagger}{\overset{\_}{y}}_{f}} = {\left( {{\overset{\sim}{\overset{\sim}{C}}}^{H}\overset{\sim}{\overset{\sim}{C}}} \right)^{- 1}{\overset{\sim}{\overset{\sim}{C}}}^{H}{\overset{\_}{y}}_{f}}}} & 2.14\end{matrix}$

Next, {tilde over (ĥ)}₁ and {tilde over (ĥ)}₂ are used to estimate IQ DCoffset d with a feedback cancellation technique according to Equation2.15:

$\begin{matrix}\begin{matrix}{\overset{\sim}{y} = {y - \left( {{\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}}} \right)}} \\{= {{dDh}_{1} + {d^{*}{Dh}_{2}}}}\end{matrix} & 2.15\end{matrix}$

wherein h₁ and h₂ can be estimated with {tilde over (ĥ)}₁ and {tildeover (ĥ)}₂. According to Equation 2.5 and Equation 2.6, {tilde over(ĥ)}₁ and {tilde over (ĥ)}₂ are multiplied by diag{e₀*,e⁻¹*, . . .,e_(−L)*} and diag{e₀*,e⁻¹*, . . . ,e_(−L)*}; {tilde over (ĥ)}₁ and{tilde over (ĥ)}₂ are acquired from Equation 2.14. Thus are derived h₁and h₂, which are respectively expressed by Equation 2.16 and Equation2.17.

h ₁=diag{e ₀ *,e ⁻¹ *, . . . ,e _(−L) *}{tilde over (h)} ₁  2.16

h ₂=diag{e ₀ ,e ⁻¹ , . . . ,e _(−L) }{tilde over (h)} ₂  2.17

All the elements of {tilde over (y)} in Equation 2.15 are summed up toobtain Equation 2.18 and Equation 2.19:

$\begin{matrix}\begin{matrix}{z = {\sum\limits_{m = 1}^{N}\; {\overset{\sim}{y}\left( {n,m} \right)}}} \\{= {{d{\overset{\sim}{\overset{\sim}{h}}}_{1}} + {d^{*}{\overset{\sim}{\overset{\sim}{h}}}_{2}}}}\end{matrix} & 2.18 \\{{{\overset{\sim}{\overset{\sim}{h}}}_{i} = {\sum\limits_{m = 1}^{N}\; {\overset{\sim}{\overset{\sim}{h}}}_{i,m}}},{i = 1},2} & 2.19\end{matrix}$

wherein {tilde over (y)}(n,m) is the mth element of the nth symbol ofthe received signal, and wherein {tilde over ({tilde over (h)})}_(i,m)is the mth element of h_(i), and wherein {tilde over ({tilde over(h)})}_(i)=Dh_(i).

In order to express IQ DC offset with the real part and imaginary part,IQ DC offset is expressed by Equation 2.20 and Equation 2.21:

$\begin{matrix}{\begin{bmatrix}z_{I} \\z_{Q}\end{bmatrix} = {\underset{\begin{matrix} \\\overset{\sim}{\overset{\sim}{H}}\end{matrix}}{\begin{bmatrix}{{\overset{\sim}{\overset{\sim}{h}}}_{1,I} + {\overset{\sim}{\overset{\sim}{h}}}_{2,I}} & {{\overset{\sim}{\overset{\sim}{h}}}_{2,Q} - {\overset{\sim}{\overset{\sim}{h}}}_{1,Q}} \\{{\overset{\sim}{\overset{\sim}{h}}}_{1,Q} + {\overset{\sim}{\overset{\sim}{h}}}_{2,Q}} & {{\overset{\sim}{\overset{\sim}{h}}}_{1,I} - {\overset{\sim}{\overset{\sim}{h}}}_{2,I}}\end{bmatrix}}\begin{bmatrix}d_{I} \\d_{Q}\end{bmatrix}}} & 2.20 \\{\begin{bmatrix}{\hat{d}}_{I} \\{\hat{d}}_{Q}\end{bmatrix} = {{\overset{\sim}{\overset{\sim}{H}}}^{- 1}\begin{bmatrix}z_{I} \\z_{Q}\end{bmatrix}}} & 2.21\end{matrix}$

wherein z=z_(I)+jz_(Q), {tilde over ({tilde over (h)})}_(i)={tilde over({tilde over (h)})}_(i,I)+j{tilde over ({tilde over (h)})}_(i,Q), i=1,2, and d=d_(I)+jd_(Q).

Further, the reconstructed IQ DC offset signal is subtracted from thereceived signal, and the residual signal is expressed by Equation 2.22which is equal to Equation 1.1 in Part I.

$\begin{matrix}\begin{matrix}{\overset{\_}{y} = {y - \left( {{{h_{1} \otimes d}\; 1} + {{h_{2} \otimes d^{*}}1}} \right)}} \\{= {y - \left( {{dDh}_{1} + {d^{*}{Dh}_{2}}} \right)}} \\{= {{h_{1} \otimes \overset{\sim}{u}} + {h_{2} \otimes {\overset{\sim}{u}}^{*}}}}\end{matrix} & 2.22\end{matrix}$

Then, the estimated {tilde over (ĥ)}₁ and {tilde over (ĥ)}₂ are used toequalize the received SC-FDMA signal. As DC offset and multipath channelhave been estimated and compensated in Equation 2.22, Equation 2.22 isidentical to Equation 1.1. Therefore, the equalization scheme expressedby Equations 1.12-1.18 in Part I can be used to restore the originaltransmitted data û.

The received SC-FDMA signal not only can be equalized in the time domainbut also can be equalized in the frequency domain for lower computationcomplexity. There are only joint IQ imbalance and shaping filterimbalance remaining in Equation 2.22 after IQ DC offset has beeneliminated. In other words, the remaining problem is the same as that ofEquation 2.19 without IQ DC offset and can be processed with the samefrequency-domain equalizer. According to Equation 2.22, Equations1.19-1.31 can be used to acquire the original transmitted signal.

After Part I and Part II, a joint estimation and compensationarchitecture of IQ imbalance, shaping filter imbalance, DC offset,multipath channel, and carrier frequency offset (CFO), which can removeall the effects of IQ mismatches caused by a direct-conversiontransceiver, will be described in Part III.

The received signal {tilde over (y)}, which has been expressed byEquation 2.1 is presented again herein as Equation 3.1. Equation 3.1involves all the factors discussed above, including IQ imbalance,shaping filter imbalance, DC offset, and multipath channel. Consideringthe CFO effect, the received signal can be expressed as Equation 3.2with the symbols thereof respectively defined by Equations 3.3-3.5.

$\begin{matrix}{\overset{\sim}{y} = {{h_{1} \otimes \left( {\overset{\sim}{u} + {d\; 1}} \right)} + {h_{2} \otimes \left( {{\overset{\sim}{u}}^{*} + {d^{*}1}} \right)}}} & 3.1 \\\begin{matrix}{y = {{\varphi (ɛ)}{\Psi (ɛ)}\overset{\sim}{y}}} \\{= {{\Psi (ɛ)}\left\{ {{{\overset{\sim}{h}}_{1} \otimes \left( {\overset{\sim}{u} + {d\; 1}} \right)} + {{\overset{\sim}{h}}_{2} \otimes \left( {{\overset{\sim}{u}}^{*} + {d^{*}1}} \right)}} \right\}}}\end{matrix} & 3.2 \\{{\varphi (ɛ)} = ^{j{({{2{{\pi ɛ}{({N + G})}}n\text{/}N} + \theta})}}} & 3.3 \\{{\Psi (ɛ)} = {{diag}\left\{ {1,^{j\; 2{\pi ɛ}\; 1\text{/}N},\cdots,^{j\; 2{\pi ɛ}\; {({N - 1})}\text{/}N}} \right\}}} & 3.4 \\{{{\overset{\sim}{h}}_{1} = {{\varphi (ɛ)}h_{1}}}{{\overset{\sim}{h}}_{2} = {{\varphi (ɛ)}h_{2}}}} & 3.5\end{matrix}$

Wherein θ is the initial phase, ε the normalized CFO, such asε=Δf_(CFO)NT_(s), and wherein imbalance parameters h₁ and h₂ aremultiplied by φ(ε) and the products are respectively expressed by {tildeover (h)}₁ and {tilde over (h)}₂.

Herein, the initial CFO is compensated in two parts, i.e. the initialfractional CFO and the initial integral CFO. A neighboring and identicalDMRS training sequence and a correlation are used to estimate theinitial fractional CFO, which is denoted by ε_(F), according to Equation3.6 and Equation 3.7:

$\begin{matrix}\begin{matrix}{\overset{\sim}{z} = {\sum\limits_{m = 1}^{N}\; {{y^{*}\left( {{n\left( {N + G} \right)} + G + m} \right)} \cdot {y\left( {{\left( {n + K} \right)\left( {N + G} \right)} + G + m} \right)}}}} \\{= {\left\{ {\sum\limits_{m = 1}^{N}\; {\alpha \left( {n,m} \right)}} \right\} \cdot ^{{j2\pi}\; {K{({N + G})}}}}} \\{= {\overset{\sim}{\alpha} \cdot ^{j\; 2\pi \; {K{({N + G})}}}}}\end{matrix} & 3.6 \\{{\hat{ɛ}}_{F} = {\frac{1}{2\pi \; {K\left( {N + G} \right)}}\measuredangle \overset{\sim}{z}}} & 3.7\end{matrix}$

Wherein {tilde over (α)} is a related channel response with a magnitudeeffect, N is the block size of each DMRS symbol, G is the length of CP,K is the number of symbols, and m is the index of the nth symbol.

The estimated initial fractional CFO, such as ε_(F), can be used tocompensate the received signal according to Equation 3.8.

y =φ*({circumflex over (ε)}_(F))Ψ*({circumflex over (ε)}_(F))y  3.8

wherein y is the received signal with the integral CFO after thereceived signal has been compensated for the fractional CFO, and whereinε_(I) can be expressed as ε_(I)=ε−ε_(F).

The received signal without the initial fractional CFO can be rewrittenas Equation 3.9:

y =Ψ(ε_(I)){{tilde over (h)} ₁*

(ũ+d1)+{tilde over (h)} ₂

(ũ*+d*1)}  3.9

wherein {tilde over (h)}₁=φ(ε_(I))h₁ and {tilde over (h)}₂=φ(ε_(I))h₂.

The other CFO compensation architecture is involved with the estimationof the initial integral CFO. Similarly, a DMRS training sequence is usedto estimate the initial integral CFO. According to Equation 3.9, thereceived signal can be derived into Equation 3.10:

$\begin{matrix}\begin{matrix}{\overset{\_}{y} = {{\Psi \left( ɛ_{I} \right)}\left\{ {{{\overset{\sim}{h}}_{1} \otimes \overset{\sim}{c}} + {{\overset{\sim}{h}}_{2} \otimes {\overset{\sim}{c}}^{*}} + {{{\overset{\sim}{h}}_{1} \otimes d}\; 1} + {{{\overset{\sim}{h}}_{2} \otimes d^{*}}1}} \right\}}} \\{= {{\Psi \left( ɛ_{I} \right)}\left\{ {{C{\overset{\sim}{h}}_{1}} + {C^{*}{\overset{\sim}{h}}_{2}} + {{dD}{\overset{\sim}{h}}_{1}} + {d^{*}D{\overset{\sim}{h}}_{2}}} \right\}}}\end{matrix} & 3.10\end{matrix}$

Wherein ε_(I) is few candidate integral CFOs within the maximum CFOregion. ε_(I) can be expressed by Equation 3.11:

$\begin{matrix}{{ɛ_{I} = {I \cdot {\Delta ɛ}}}{wherein}} & 3.11 \\{{\Delta ɛ} = {{\left( {\frac{1}{2\pi \; {K\left( {N + G} \right)}T_{S}} \times \pi} \right)\text{/}\frac{1}{{NT}_{S}}} = \frac{N}{2{K\left( {N + G} \right)}}}} & 3.12 \\{\left\lceil {{- ɛ_{\max,{CFO}}}\text{/}{\Delta ɛ}} \right\rceil < I < \left\lceil {ɛ_{\max,{CFO}}\text{/}{\Delta ɛ}} \right\rceil} & 3.13\end{matrix}$

wherein ε_(max,CFO) denotes the maximum CFO value.

The values of K, N and G in Equation 3.12 are known, Δε can be obtained.Therefore, the integral CFO (ε_(I)) is acquired.

With the known integral CFO, IQ DC offset can be removed with thefrequency-domain estimation method that has been described in Part II.The post-FFT received signal can be obtained according to Equation 3.14:

$\begin{matrix}\begin{matrix}{{\overset{\_}{y}}_{f} = {F\overset{\_}{y}}} \\{{= {{F\; {\Psi \left( ɛ_{I} \right)}\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {F\; {\Psi \left( ɛ_{I} \right)}{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}} +}}} \\{{{{dF}\; {\Psi \left( ɛ_{I} \right)}{DF}^{H}F{\overset{\sim}{h}}_{1}} + {d^{*}F\; {\Psi \left( ɛ_{I} \right)}{DF}^{H}F{\overset{\sim}{h}}_{2}}}}\end{matrix} & 3.14\end{matrix}$

wherein the definitions of the parameters are the same as thosementioned above. In other words, Equation 3.14 equals Equation 2.7multiplied by the integral CFO. Ψ _(f) (ε_(I)) can be expressed asEquation 3.15:

$\begin{matrix}\begin{matrix}{{{\overset{\_}{\Psi}}_{f}\left( ɛ_{I} \right)} = {F\; {\Psi \left( ɛ_{I} \right)}{DF}^{H}}} \\{= {F\; {\Psi \left( ɛ_{I} \right)}F^{H}{FDF}^{H}}} \\{= \left\lbrack \begin{matrix}{\overset{\sim}{\lambda}}_{1} \\{\overset{\sim}{\lambda}}_{2} \\\vdots\end{matrix} \middle| O \right\rbrack} \\{= \left\lbrack {\overset{\_}{\psi}}_{f,I} \middle| O_{N \times {({N - 1})}} \right\rbrack}\end{matrix} & 3.15\end{matrix}$

wherein FDF^(H)=diag{λ_(DC), 0, 0, . . . }, and wherein ψ _(f,I) is thefirst column vector that denotes the IQ DC offset with a CFO effect, andwherein Ψ _(f) is a rectangular matrix with the first column vectorbeing non-zero and the other columns being zero. ψ _(f,I) can beremoved, which means that the IQ DC offset with the integral CFO effectis eliminated.

In the same way to remove IQ DC offset as Equation 2.9, the post-FFTreceived data is multiplied by a matrix T_(I) to remove the first columnvector which is the IQ DC offset with the Ith integral CFO effectaccording to Equation 3.16.

$\begin{matrix}\begin{matrix}{{\overset{\_}{y}}_{f,I} = {T_{I}F\overset{\_}{y}}} \\{= {{F_{T,I}{\Psi \left( ɛ_{I} \right)}\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {F_{T,I}{\Psi \left( ɛ_{I} \right)}{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}} + {{dT}_{I}{{\overset{\_}{\Psi}}_{f}\left( ɛ_{I} \right)}F{\overset{\sim}{h}}_{1}} +}} \\{{d^{*}T_{I}{{\overset{\_}{\Psi}}_{f}\left( ɛ_{I} \right)}F{\overset{\sim}{h}}_{2}}}\end{matrix} & 3.16\end{matrix}$

wherein the parameters in Equation 3.16 are respectively defined byEquations 3.17-3.20:

F _(T,I) =T _(I) F  3.17

T _(I) =I−ψ _(f,I)·ψ*_(f,I)  3.18

ψ_(f,I)=ψ _(f,I)/norm(ψ _(f,I))  3.19

T _(I) Ψ _(f)(ε_(I))=O _(N×N)  3.20

O_(N×N) is an N by N matrix of all zeros, which indicates that IQ DCoffset has been removed in Equation 3.19. ε_(I) is a predefinedcandidate integral CFO. Thus, ψ _(f,I) can be obtained beforehand. Asthe IQ DC offset effect caused by the integral CFO transferred toanother subcarrier wave, the position of the two largest magnitudes of ψ_(f,I) can be monitored. Then, a T_(I) blocking matrix is constructed toeliminate the influence of IQ DC offset, which will favor the search ofthe integral CFO. The T_(I) matrix is dependent on the largest indicesof ψ _(f,I) magnitudes. In different conditions, T_(I) is respectivelyexpressed by Equations 3.21-3.23:

T _(I) =[O _((N−2)×2)

I _((N−2)×(N−2))]_((N−2)×N)  3.21

for the first two largest subcarriers;

T _(I) =[I _((N−2)×(N−2))

O _((N−2)×2)]_((N−2)×N)  3.22

for the last two largest subcarriers; and

T _(I) =[O _((N−2)×1)

I _((N−2)×(N−2))

O _((N−2)×1)]_((N−2)×2)  3.23

for the first and the last largest subcarriers.

In order to find the correct Ith candidate integral CFO for removing IQDC offset, the frequency-domain received signal can be expressed byEquation 3.24:

$\begin{matrix}{\begin{matrix}{{\overset{\_}{y}}_{f,I} = {{F_{T,I}{\Psi \left( ɛ_{I} \right)}\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {F_{T,I}{\Psi \left( ɛ_{I} \right)}{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}}}} \\{= {{\overset{\sim}{\overset{\sim}{C}}}_{I}\overset{\sim}{h}}}\end{matrix}{wherein}} & 3.24 \\{{\overset{\sim}{\overset{\sim}{C}}}_{I} = \begin{bmatrix}{F_{T,I}{\Psi \left( ɛ_{I} \right)}\overset{\sim}{C}} & {F_{T,I}{\Psi \left( ɛ_{I} \right)}{\overset{\sim}{C}}^{*}}\end{bmatrix}} & 3.25 \\{\overset{\sim}{h} = \begin{bmatrix}{\overset{\sim}{h}}_{1}^{T} & {\overset{\sim}{h}}_{2}^{T}\end{bmatrix}^{T}} & 3.26\end{matrix}$

wherein {tilde over ({tilde over (C)})}_(I) is a composite trainingsequence, andwherein F_(T,I) C _(I)={tilde over ({tilde over (C)})}_(I) and C_(I)=Ψ(ε_(I))[{tilde over (C)}{tilde over (C)}*].

The composite response {tilde over (h)} can be estimated with an LSmethod according to Equation 3.27:

$\begin{matrix}\begin{matrix}{\hat{\overset{\sim}{h}} = {{\overset{\sim}{\overset{\sim}{C}}}_{I}^{\dagger}{\overset{\_}{y}}_{f,I}}} \\{= {\left( {{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\sim}{\overset{\sim}{C}}}_{I}} \right)^{- 1}{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\_}{y}}_{f,I}}}\end{matrix} & 3.27\end{matrix}$

Next, {tilde over (ĥ)} is substituted into y _(f,I) to obtain theprojected received signal ŷ _(f,I) expressed by Equation 3.28:

$\begin{matrix}{{\hat{\overset{\_}{y}}}_{f,I} = {\underset{\underset{Projection}{}}{{{\overset{\sim}{\overset{\sim}{C}}}_{I}\left( {{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\sim}{\overset{\sim}{C}}}_{I}} \right)}^{- 1}{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}}{\overset{\_}{y}}_{f,I}}} & 3.28\end{matrix}$

In order to find the correct I, i.e. ε_(I), the error distance betweenthe post-FFT received signal y _(f,I) and the projected received signalŷ _(f,I) is minimized according to Equation 3.29.

$\begin{matrix}\begin{matrix}{{\min\limits_{I}{{{\overset{\_}{y}}_{f,I} - {\hat{\overset{\_}{y}}}_{f,I}}}^{2}} = {\min\limits_{I}{{{\overset{\_}{y}}_{f,I} - {{{\overset{\sim}{\overset{\sim}{C}}}_{I}\left( {{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\sim}{\overset{\sim}{C}}}_{I}} \right)}^{- 1}{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\_}{y}}_{f,I}}}}^{2}}} \\{= {\min\limits_{I}{{{\overset{\_}{y}}_{f,I}^{H}\left\lbrack {I - {{{\overset{\sim}{\overset{\sim}{C}}}_{I}\left( {{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\sim}{\overset{\sim}{C}}}_{I}} \right)}^{- 1}{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}}} \right\rbrack}{\overset{\_}{y}}_{f,I}}}} \\{= {\max\limits_{I}{{\overset{\_}{y}}_{f,I}^{H}{{\overset{\sim}{\overset{\sim}{C}}}_{I}\left( {{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\sim}{\overset{\sim}{C}}}_{I}} \right)}^{- 1}{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\_}{y}}_{f,I}}}}\end{matrix} & 3.29\end{matrix}$

According to the abovementioned algorithm, the integral CFO can bedetermined via finding the maximum of Equation 3.30:

$\begin{matrix}{{\hat{ɛ}}_{I} = {\arg \mspace{14mu} {\max\limits_{I}\mspace{14mu} {{\overset{\_}{y}}^{H}F_{T,I}^{H}F_{T,I}{{\overset{\_}{C}}_{I}\left( {{\overset{\_}{C}}_{I}^{H}F_{T,I}^{H}F_{T,I}{\overset{\_}{C}}_{I}} \right)}^{- 1}{\overset{\_}{C}}_{I}^{H}F_{T,I}^{H}F_{T,I}\overset{\_}{y}}}}} & 3.30\end{matrix}$

wherein y is the original received signal with the initial fractionalCFO compensation, F_(T,I) is a transform matrix with IQ DC offsetremoval, C _(I) is the known training sequence matrix with candidateintegral CFO rotation.

The present invention further provides another method to undertakeintegral CFO searching, wherein the integral CFO is found via nullingthe DC component and searching the projection of the residual power ofIQ DC offset. According to Equation 3.29, the integral CFO can bedetermined with the abovementioned algorithm. However, nulling thetransform T_(I) is to remove the DC component, which will transform ordeform the other subcarrier waves. Therefore, the minimization ML schemecannot find the correct integral CFO in the output power of all thesubcarrier waves. In order to overcome the problem, the presentinvention proposes a minimization ML scheme, which is adaptive tospecified DC subcarrier output power and expressed by Equation 3.31. Thenulling transforms are for different integral CFOs. If the nullingtransform matches the integral CFO of the received DC component signal,the minimum output power of the DC carrier wave can be acquired, and thecorrect integral CFO can be found.

$\begin{matrix}\begin{matrix}{ɛ_{I} = {\arg \mspace{14mu} {\min\limits_{ɛ_{I}}\; {e_{m}^{H}\left\{ {{diag}\left( {\overset{\_}{y}}_{f,I}^{H} \right)} \right.}}}} \\{\left. {\left\lbrack {I - {{{\overset{\sim}{\overset{\sim}{C}}}_{I}\left( {{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}{\overset{\sim}{\overset{\sim}{C}}}_{I}} \right)}^{- 1}{\overset{\sim}{\overset{\sim}{C}}}_{I}^{H}}} \right\rbrack {{diag}\left( {\overset{\_}{y}}_{f,I} \right)}} \right\} e_{m}} \\{= {\arg \mspace{14mu} {\min\limits_{ɛ_{I}}\; {e_{m}^{H}\left\{ {{diag}\left( {{\overset{\_}{y}}^{H}F_{T,I}^{H}} \right)} \right.}}}} \\{\left. {\left\lbrack {I - {F_{T,I}{{\overset{\_}{C}}_{I}\left( {{\overset{\_}{C}}_{I}^{H}F_{T,I}^{H}F_{T,I}{\overset{\_}{C}}_{I}} \right)}^{- 1}{\overset{\_}{C}}_{I}^{H}F_{T,I}^{H}}} \right\rbrack {{diag}\left( {F_{T,I}\overset{\_}{y}} \right)}} \right\} e_{m}}\end{matrix} & 3.31\end{matrix}$

wherein e_(m)=[0, 0, . . . , 0, 1, 0, . . . , 0, 0]^(T) with the mthelement being assigned 1, and wherein m is the DC carrier index due tothe DC component being shifted by the integral CFO. Because thecandidate integral CFO has been pre-defined, the definitions of y andF_(T,I) are the same as in Equation 3.30. The index m can bepredetermined by the largest magnitude component of the IQ DC offsetvector ψ _(f,I) as shown in Equation 3.32.

$\begin{matrix}{{m = {\arg \mspace{14mu} {\max\limits_{m}{{{\overset{\_}{\psi}}_{f,I}(m)}}}}},{0 \leq m \leq {N - 1}}} & 3.32\end{matrix}$

After the integral CFO is estimated, the complete CFO is acquired, suchas {circumflex over (ε)}={circumflex over (ε)}_(F)+{circumflex over(ε)}_(I). Then, the received signal can be compensated with {circumflexover (ε)} according to Equation 3.33:

$\begin{matrix}\begin{matrix}{\overset{\_}{y} = {{\varphi^{*}\left( \hat{ɛ} \right)}{\Psi^{*}\left( \hat{ɛ} \right)}y}} \\{\approx {{{\overset{\sim}{h}}_{1} \otimes \left( {\overset{\sim}{u} + {d\; 1}} \right)} + {{\overset{\sim}{h}}_{2} \otimes \left( {{\overset{\sim}{u}}^{*} + {d^{*}\; 1}} \right)}}}\end{matrix} & 3.33\end{matrix}$

wherein the initial phases are merged into h₁ and h₂ according toEquation 3.34:

{tilde over (h)} ₁ =e ^(jθ) h ₁

{tilde over (h)} ₂ =e ^(jθ) h ₂  3.34

Assuming the CFO compensation is perfect, the received signal only hasIQ imbalance, shaping filter imbalance, multipath channel, and IQ DCoffset (i.e. Equation 3.33). Then, the estimation and compensationmethod of Part II can be used herein, and the original transmittedsignal (û) will be checked.

If CFO is not estimated perfectly, partial decision-directed symbols iican be used to undertake better estimation (Δ{circumflex over (ε)}) ofCFO and other imperfection parameters according to Equation 3.35 andEquation 3.36:

$\begin{matrix}\begin{matrix}{\overset{\_}{z} = {\sum\limits_{n = {K + 1}}^{K + Q}\; {\left( {{{\hat{s}}^{H}(n)}{\overset{\_}{y}(n)}} \right)^{*}\left( {{{\hat{s}}^{H}\left( {n + Q} \right)}{\overset{\_}{y}\left( {n + Q} \right)}} \right)}}} \\{= {\overset{\_}{\alpha}^{{j2}\; {\pi\Delta ɛ}\; {Q{({M + G})}}}}}\end{matrix} & 3.35 \\{{\Delta \; \hat{ɛ}} = {\frac{1}{2\; \pi \; {Q\left( {M + G} \right)}}\measuredangle \overset{\_}{z}}} & 3.36\end{matrix}$

wherein Q denotes the size of the related block symbol of the currentsymbol block, and wherein α denotes the related channel response with amagnitude of time-invariant environment, and wherein ŝ is thereconstructed decision-directed symbol expressed by Equation 3.37.

ŝ=ĥ ₁

({tilde over ({circumflex over (u)})}+d1)+ĥ ₂

({tilde over ({circumflex over (u)})}*+{circumflex over (d)}*1)  3.37

If the performance of EVM (Error Vector Magnitude) is not good enough,the present invention may further use the reconstructeddecision-directed symbols (ŝ) to estimate and compensate RFimperfections until the performance of EVM converges.

Similarly, the present invention may also use the frequency-domainequalizer to reduce the computational complexity. Herein, the entire RFimperfections and channel environment is taken into consideration, asshown in FIG. 2. The RF imperfections and channel environment will beestimated and compensated step by step. After CFO compensation, theresidual problem can be solved in the way as in Part II. In other words,the abovementioned method can be used to estimate and compensate theresidual RF imperfections easily.

After Equation 3.33, the process will return to Equation 2.1 andcontinue to use the estimation and compensation method of Part II toequalize the received signal. Then, the original demodulation data isestimated similarly to Equations 1.19-1.31, which have been demonstratedabove and will not repeat herein.

As shown in the flowchart of FIG. 2, the joint estimation andcompensation method of the present invention sequentially solves theproblems of CFO, DC offset, multipath channel, IQ imbalance and shapingfilter imbalance so as to remove the influence of IQ mismatches causedby the direction-conversion transceiver and effectively estimate andcompensate RF mismatches in an LTE uplink system. The present inventioncan further take different RF decays into consideration and undertakethe joint estimation and compensation of the RF decays in the timedomain. Thereby, the present invention improves the performance of theLTE uplink system furthermore.

After the technical contents and efficacies of the present invention arefully demonstrated above, the results of the present invention will becompared with the results of the LTE signal analyzer 46 of aninternational company Rohde & Schwarz (R&S), as shown in FIG. 3. The LTEsignal analyzer 48 used by the present invention includes an AgilentE4406A down converter 482 and a computer 484. Firstly, use an R&S vectorsignal generator (VSG) 40 to transmit a standard uplink signal. Achannel emulator 42 is used to generate a multipath channel. The signalis respectively transmitted by a power divider 44 to the R&S LTE signalanalyzer 46 and the LTE signal analyzer 48 of the present invention forperformance comparison.

Next, the VSG 40 is used to set RF imperfection parameters, includingI-channel DC offset: 10%, Q-channel DC offset: −5.1%, magnitudeimbalance: 1 dB, phase imbalance: 10 degrees, and central carrierfrequency: 1.85001 GHz so as to generate 10 KHz CFO. The channelemulator 42 is set to meet the ITU standard: time lags: 0, 110, 190, and410 ns; average powers of the paths: 0, −9.7, −19.2, and −22.8 dB.

The analysis of the measurement results of the R&S LTE signal analyzer46 is shown in FIG. 4(a) and FIG. 4(b), which are respectively EVM(Error Vector Magnitude) and the constellation map of the performanceanalysis results of the R&S LTE signal analyzer 46. Owing to RFimperfections and multipath channel, the EVM performance decline is asmuch as 10%. Contrarily, the joint estimation and compensation method ofthe present invention still has a superior performance of only 1% EVM,as shown in FIG. 5(a), FIG. 5(b), and FIG. 6. FIG. 5(a) and FIG. 5(b)respectively show the constellation maps of PUSCH signals and DMRSsignals of the present invention. FIG. 6 shows the captured image of EVMperformance of PUSCH signals and DMRS signals of the present invention.Thus is proved that the joint estimation and compensation method of thepresent invention not only meets the LTE standard but also has superiorsignal reception quality in adverse environments.

The technical contents and characteristics of the present invention havebeen fully demonstrated with the embodiments to enable the personsskilled in the art to understand, make, and use the present inventionhereinbefore. However, these embodiments are only to exemplify thepresent invention but not to limit the scope of the present invention.Any equivalent modification or variation according to the spirit of thepresent invention is to be also included within the scope of the presentinvention.

1. A joint estimation and compensation method of RF imperfections in aLTE uplink system, comprising steps: establishing a joint signal modelwith RF imperfections; according to said joint signal model, undertakingan initial CFO (Carrier Frequency Offset) estimation of a receivedsignal in a time domain so as to estimate CFO parameters and compensatesaid received signal; undertaking a joint estimation of DC offset,multipath channel and imbalance signals of said joint signal model ofsaid received signal, compensating said received signal in said timedomain, and acquiring imbalance parameters of said imbalance signals;and determining modulation data to acquire an original transmittedsignal.
 2. The joint estimation and compensation method according toclaim 1 further comprising: determining whether error vector magnitudeconverges; if yes, undertaking a next step; if no, using adecision-directed symbol to undertake iterative CFO estimation andcompensation so as to undertake further estimation and compensation ofsaid RF imperfections until said error vector magnitude converges; andestimating gain mismatch parameters and phase mismatch parameters ofsaid joint signal model according to said imbalance parameters.
 3. Thejoint estimation and compensation method according to claim 2, whereinsaid initial CFO estimation includes steps: using a training sequence toestimate an initial fractional CFO so as to compensate said receivedsignal; estimating an initial integral CFO so as to acquire a value ofsaid initial integral CFO; and using a frequency estimation method toremove said CFO of said received signal.
 4. The joint estimation andcompensation method according to claim 3, wherein said joint signal ofsaid received signal is expressed by $\begin{matrix}{y = {{\varphi (ɛ)}{\Psi (ɛ)}\overset{\sim}{y}}} \\{{= {{\Psi (ɛ)}\left\{ {{{\overset{\sim}{h}}_{1} \otimes \left( {\overset{\sim}{u} + {d\; 1}} \right)} + {{\overset{\sim}{h}}_{2} \otimes \left( {{\overset{\sim}{u}}^{*} + {d^{*}\; 1}} \right)}} \right\}}},}\end{matrix}$ and wherein φ(ε)=e^(j(2πε(N+G)n/N+θ), Ψ(ε)=diag{)1,e_(j2πε1/N), . . . e^(j2πε(N−1)/N)}, and h₁ and h₂ are multiplied byφ(ε) to obtain {tilde over (h)}₁=φ(ε)h₁ {tilde over (h)}₂=φ(ε)h₂, andwherein θ is an initial phase, and s is a normalized CFO, and wherein Nis a block size of a DMRS (demodulation reference signal) symbol, G is alength of cyclic prefixes, and N=0, 1, . . . N−1.
 5. The jointestimation and compensation method according to claim 3, wherein saidfrequency estimation method converts said received signal into apost-FFT (Fast Fourier Transform) received signal and then removes saidCFO from said post-FFT received signal.
 6. The joint estimation andcompensation method according to claim 3, wherein in said step ofestimating said initial integral CFO, said integral CFO is determinedvia finding a maximum of${{\hat{ɛ}}_{I} = {\arg \mspace{11mu} {\max\limits_{I}{{\overset{\_}{y}}^{H}F_{T,I}^{H}F_{T,I}{{\overset{\_}{C}}_{I}\left( {{\overset{\_}{C}}_{I}^{H}F_{T,I}^{H}F_{T,I}{\overset{\_}{C}}_{I}} \right)}^{- 1}{\overset{\_}{C}}_{I}^{H}F_{T,I}^{H}F_{T,I}\overset{\_}{y}}}}},$wherein y is an original received signal with initial fractional CFObeing compensation, F_(T,I) is a transform matrix with DC offsetremoval, C _(I) is a known training sequence matrix with a candidateintegral CFO.
 7. The joint estimation and compensation method accordingto claim 3, wherein said integral CFO is estimated via nulling a DCcomponent and searching a projection of residual power of said DCoffset.
 8. The joint estimation and compensation method according toclaim 2, wherein partial decision-directed symbols are used to undertakesaid iterative CFO estimation.
 9. The joint estimation and compensationmethod according to claim 8, wherein said iterative CFO estimation isundertaken according to following equations: $\begin{matrix}\begin{matrix}{\overset{\_}{z} = {\sum\limits_{n = {K + 1}}^{K + Q}\; {\left( {{{\hat{s}}^{H}(n)}{\overset{\_}{y}(n)}} \right)^{*}\left( {{{\hat{s}}^{H}\left( {n + Q} \right)}{\overset{\_}{y}\left( {n + Q} \right)}} \right)}}} \\{= {\overset{\_}{\alpha}^{{j2}\; {\pi\Delta ɛ}\; {Q{({M + G})}}}}}\end{matrix} \\{{\Delta \; \hat{ɛ}} = {\frac{1}{2\; \pi \; {Q\left( {M + G} \right)}}\measuredangle \overset{\_}{z}}}\end{matrix}$ wherein Q is dependent on a size of a related block symbolof a current symbol block, and wherein α is a related channel response,and wherein ŝ is said decision-directed symbol.
 10. The joint estimationand compensation method according to claim 9, wherein saiddecision-directed symbol ŝ is expressed by ŝ=ĥ₁

({tilde over (û)}+{circumflex over (d)}1)+{tilde over (h)}₂

({tilde over (û)}*+{circumflex over (d)}*1), wherein h₁ and h₂ areimbalance parameters, u is an estimated original signal, and d is anestimated DC offset.
 11. The joint estimation and compensation methodaccording to claim 2, wherein said joint signal model of said receivedsignal y with CFO compensation is expressed by y=h₁

(ũ+d1)+h₂

(ũ*+d*1) wherein h₁ and h₂ are imbalance coefficients involving IQimbalance and shaping filter imbalance, and wherein d denotes DC offset,and Vector I is all N×1 vectors, and wherein h₁ and h₂ involve a realpart and an imaginary part a filter imbalance parameter h_(C,I) andh_(C,Q) and wherein h_(C,I) and h_(C,Q) are convoluted with multipathchannel h_(ch) and expressed by $\left\{ {\begin{matrix}{h_{C,I} = {{Re}{\left\{ h_{RX} \right\} \otimes {Re}}\left\{ {h_{ch} \otimes h_{TX}} \right\}}} \\{h_{C,Q} = {{Im}{\left\{ h_{RX} \right\} \otimes {Im}}\left\{ {h_{ch} \otimes h_{TX}} \right\}}}\end{matrix},} \right.$ and wherein h_(RX) and h_(TX) are respectivelyshaping filters of a transmitter and a receiver.
 12. The jointestimation and compensation method according to claim 11, wherein saidDC offset and said multipath channel are estimated with a demodulationreference signal (DMRS), and wherein said received signal is expressedby a convolution matrix: $\begin{matrix}{y = {{h_{1} \otimes \overset{\sim}{c}} + {h_{2} \otimes {\overset{\sim}{c}}^{*}} + {{h_{1} \otimes d}\; 1} + {{h_{2} \otimes d^{*}}1}}} \\{{= {{\overset{\sim}{C}{\overset{\sim}{h}}_{1}} + {{\overset{\sim}{C}}^{*}{\overset{\sim}{h}}_{2}} + {d\; {Dh}_{1}} + {d^{*}{Dh}_{2}}}},}\end{matrix}$ wherein D is a circular convolution matrix of all 1vectors, and wherein {tilde over (C)} is an N by L+1 circularconvolution matrix generated by a training sequence {tilde over (c)}with Δf=½ offset, and wherein {tilde over (h)}₁=diag{e₀, e⁻¹, . . .,e_(−L)}h₁ and {tilde over (h)}₂=diag{e₀*,e⁻¹*, . . . ,e_(−L)*}h₂. 13.The joint estimation and compensation method according to claim 12,wherein said step of using said training sequence to estimate said DCoffset and said multipath channel of said joint signal model of saidreceived signal further includes steps: converting said received signalinto a post-FFT received signal in a frequency-domain; multiplying saidpost-FFT received signal with a zero matrix to eliminate said DC offsetand acquire said received signal in said frequency-domain; using a leastsquare and a feedback cancellation technique to estimate a reconstructedDC offset signal; and subtracting said reconstructed DC offset signalfrom said received signal to obtain a residual expressed by y=h₁

ũ+h₂

ũ*.
 14. The joint estimation and compensation method according to claim2, wherein said imbalance signals include an IQ imbalance signal and ashaping filter imbalance signal.
 15. The joint estimation andcompensation method according to claim 14, wherein said received signalwith said CFO, said DC offset, said multipath channel having beenestimated and compensated is said joint signal model with imbalancesignals, which is expressed by y=h₁

ũ+h₂

ũ*, and wherein h₁ and h₂ are said imbalance parameters with IQimbalance and shaping filter imbalance, and wherein ũ is an originalsignal with Δf=½.
 16. The joint estimation and compensation methodaccording to claim 15, wherein a demodulation reference signal is usedas said training sequence and expressed by${\overset{\sim}{C} = {E\begin{bmatrix}{c(0)} & {c\left( {N - 1} \right)} & \ldots & {c(1)} \\{c(1)} & {c(0)} & \ldots & {c(2)} \\\vdots & \vdots & \ddots & \vdots \\{c\left( {N - 1} \right)} & {c\left( {N - 2} \right)} & \ldots & {c(0)}\end{bmatrix}}_{N \times L}},$ wherein E=diag{e₀, e₁, . . . , e_(N−1)}is a diagonal matrix with Δf=½ offset, and wherein {tilde over(c)}=[{tilde over (c)}(0){tilde over (c)}(1) . . . {tilde over(c)}(N−1)] is a Chu sequence with a length of N and Δf=½.
 17. The jointestimation and compensation method according to claim 16, wherein apseudo inverse matrix is used to estimate said imbalance parameters ofsaid imbalance signals.
 18. The joint estimation and compensation methodaccording to claim 15, wherein said gain mismatch parameter g_(T) andsaid phase mismatch parameter φ_(T) are estimated via using imbalanceparameters of IQ imbalance and shaping filter imbalance of h₁ and h₂according to an equation: $\left\{ {\begin{matrix}{h_{1} = {\frac{1}{2}\left( {h_{C,I} + {h_{C,Q}g_{T}^{j\; \varphi_{T}}}} \right)}} \\{h_{2} = {\frac{1}{2}\left( {h_{C,I} + {h_{C,Q}g_{T}^{j\; \varphi_{T}}}} \right)}}\end{matrix},} \right.$ and wherein h_(C,I) and h_(C,Q) are respectivelya real-part shaping filter imbalance parameter and an imaginary-partshaping filter imbalance parameter.
 19. The joint estimation andcompensation method according to claim 18, wherein a frequency-domainequalizer is used to equalize said received signal and reducecomputational complexity.
 20. The joint estimation and compensationmethod according to claim 19, wherein equalizing said received signalincludes steps: using a known matrix to compensate Δf=½ offset of aidreceived signal; converting said received signal in a time domain into afrequency-domain received signal; using said imbalance parameters toobtain a Δf=½ offset involving matrix of joint estimation of said IQimbalance parameter and said shaping filter imbalance parameter and ajoint RF effect parameter; and multiplying said frequency-domainreceived signal with an inverse matrix coefficient to remove said jointRF effect parameter so as to complete an equalization process and obtainan original frequency-domain transmitted signal.
 21. The jointestimation and compensation method according to claim 20, wherein aftersaid original frequency-domain transmitted signal is obtained, an IFFToperator is used to convert said original frequency-domain transmittedsignal into an original time-domain transmitted signal.